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Conjugate (square roots)

Change of the sign of a square root From Wikipedia, the free encyclopedia

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In mathematics, the conjugate of an expression of the form is provided that does not appear in a and b. One says also that the two expressions are conjugate.

In particular, the two solutions of a quadratic equation are conjugate, as per the in the quadratic formula .

Complex conjugation is the special case where the square root is the imaginary unit.

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Properties

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As and the sum and the product of conjugate expressions do not involve the square root anymore.

This property is used for removing a square root from a denominator, by multiplying the numerator and the denominator of a fraction by the conjugate of the denominator (see Rationalisation). An example of this usage is: Hence:

A corollary property is that the subtraction:

leaves only a term containing the root.

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